Geodesic
Extending $n$ times differentiable functions of several variables
Czechoslovak Mathematical Journal, Tome 49 (1999) no. 4, pp. 825-830.

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It is shown that $n$ times Peano differentiable functions defined on a closed subset of $\mathbb{R}^m$ and satisfying a certain condition on that set can be extended to $n$ times Peano differentiable functions defined on $\mathbb{R}^m$ if and only if the $n$th order Peano derivatives are Baire class one functions.
Classification : 26A21, 26B05 
@article{CMJ_1999__49_4_a12,
     author = {Fejzi\'c, Hajrudin and Rinne, Dan and Weil, Clifford},
     title = {Extending $n$ times differentiable functions of several variables},
     journal = {Czechoslovak Mathematical Journal},
     pages = {825--830},
     publisher = {mathdoc},
     volume = {49},
     number = {4},
     year = {1999},
     mrnumber = {1746707},
     zbl = {1005.26007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_1999__49_4_a12/}
}
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Fejzić, Hajrudin; Rinne, Dan; Weil, Clifford. Extending $n$ times differentiable functions of several variables. Czechoslovak Mathematical Journal, Tome 49 (1999) no. 4, pp. 825-830. http://geodesic.mathdoc.fr/item/CMJ_1999__49_4_a12/